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Question
If `vec"a" = hat"i" - 2hat"j" + 3hat"k", vec"b" = 2hat"i" + hat"j" - 2hat"k", vec"c" = 3hat"i" + 2hat"j" + hat"k"`, find `vec"a" * (vec"b" xx vec"c")`
Solution
Given `vec"a" = hat"i" - 2hat"j" + 3hat"k"`
`vec"b" = 2hat"i" + hat"j" - 2hat"k"`
`vec"c" = 3hat"i" + 2hat"j" + hat"k"`
`vec"b" xx vec"c" = |(vec"i", vec"j", vec"k"),(2, 1, -2),(3, 2, 1)|`
`vec"b" xx vec"c" = 5hat"i" - 8hat"j" + hat"k"`
`vec"a"*(vec"b" xx vec"c")` = 5 + 16 + 3 = 24
Aliter: `vec"a"*(vec"b" xx vec"c") = [vec"a" vec"b" vec"c"]`
= `|(1, -2, 3),(2, 1, -2),(3, 2, 1)|`
= 1(5) + 2(8) + 3(1)
= 4 + 16 + 3
= 24
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